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The Solubility of Organic Compounds in Supercritical CO2 Guillermo A

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The Solubility of Organic Compounds in Supercritical CO2 Guillermo A The Solubility of Organic Compounds in Supercritical CO2 Guillermo A. Alvareza, Wolfram Baumannb, Martha Bohrer Adaimeb, and Frank Neitzelb a Departamento de Qu´ımica, Facultad de Ciencias, Universidad de los Andes, Carrera 1 No. 18A-10/70, Bogot´a, Colombia b Institute of Physical Chemistry, University of Mainz, D-55099 Mainz, Germany Reprint requests to Prof. G. A. A.; Fax: 00571 3324366; E-mail: [email protected] Z. Naturforsch. 60a, 641 – 648 (2005); received May 3, 2005 A simple liquid solution model is proposed to describe the effect of solvent-solute interactions on the solubility of nonpolar and slightly polar substances in supercritical solvents. Treating the system as an ideal solution, the effect of pressure on the solubility is zero or nearly zero, as it is governed by the difference in molar volume of the pure supercooled liquid solute and the pure solid solute, and this may be nearly zero. Deviations from ideal behavior are given by activity coefficients of the Margules type with the interaction parameter w interpreted as interchange energy as in the lattice theory. The hypothesis is put forward that the interchange energy is of the same form as a function proposed by Liptay and others to describe the effect of the solvent on the wavelength of the absorption maximum of the solute dissolved in the solvent. The function consists of a radius of interaction a and a function g(ε) of the dielectric constant ε of the solvent, treated as a continuum. The function g depends on pressure through the pressure dependence of the dielectric constant ε(P). The attractive feature of this formalism, introduced by Baumann et al. and here justified thermodynamically, is that plots of the logarithm of solubility vs. g are linear, except for polar solutes near the solvent’s critical point. Changes in slope then admit interpretation as changes in the radius of interaction a with possible clues about the mechanism of solvation of these molecules. Key words: Dielectric Interactions; Solubility; Supercritical CO2; Thermodynamic Model; Activity Coefficient. 1. Introduction solvent depends nearly linearly on the density [3], one may substitute the dielectric constant ε(P) by the den- The solubility of substances in supercritical sol- sity ρ(P) as a measure of solvent-solute interactions in vents is relevant in separation processes such as su- practical cases. percritical fluid extraction and chromatography and However, we can proceed further according to the for modeling the state of a solute molecule in a sol- theories of Lippert [4], Mataga et al. [5] and no- vent [1]. In particular, since near the critical point the tably Liptay [6], who showed that in polar solvents solvent’s density can change by a factor of ten with the change due to the solvent in the wavelength at only small changes in the temperature and the pres- the maximum of absorption of light by the solute sure, it is clear that the solubility of the solute can vary or solvatochromic shift is a function of (ε(P) − 1)/ likewise by a large factor. Enormous changes in the (a3(2ε(P)+1)) = g(ε)/a3. Further, the shift in so- nature of the solvent, quantified for example by the in- lution is towards red relative to the gas phase, that terchange energy w of the lattice theory, would be re- is the solvent-solute system is stabilized by disper- quired to bring about the simple “distance” effect due sion interactions and by interactions of the dipole of to the compressibility of the solvent near the critical the molecule with the surrounding dielectric. Since the point. function ε(P) increases monotonically with P, this sta- It thus appears that the solvent’s density for a solvent bilizing effect for constant a always increases the sol- near the critical point is a suitable measure of solvent- ubility, reaching an asymptotic level at high P (but see solute interaction and hence of solubility. Accordingly, below). Thus, here the interchange energy is negative, plots of the logarithm of solubility vs. the density or leading to negative deviations of Raoult’s law, in con- the logarithm of the density obey a linear relationship trast to the usual positive deviations for nonpolar so- in many cases [2]. Since the dielectric constant of the lutes in nonpolar solvents. 0932–0784 / 05 / 0800–0641 $ 06.00 c 2005 Verlag der Zeitschrift f¨ur Naturforschung, T¨ubingen · http://znaturforsch.com 642 G. A. Alvarez et al. · Solubility in Supercritical CO2 Numerous models have been proposed for the ef- 2. Thermodynamic Model fect of the thermodynamic variables temperature T It is often the case for solutes with high melting and pressure P on the mole fraction xB of solute B in the saturated solution since the work of Schr¨oder points that solid B dissolves in liquid A at a given pres- on the effect of temperature on the solubility of naph- sure only up to a certain mole fraction xB called the thalene in benzene (see e.g. Pitzer [7]). The present equilibrium mole fraction or solubility of the solute in formalism follows the same steps of Schr¨oder but the solution saturated with the solid. For component B, considering changes of pressure instead of changes equilibrium between a solid phase s and a liquid phase of temperature. Whereas molar enthalpy is the vari- l is dictated by the equality of chemical potentials able that controls ideal solubility as a function of µs = µl . temperature, here molar volume controls ideal solu- B B (1) bility as a function of pressure. In contrast to the The chemical potential of the pure solid phase B is temperature effect, the ideal pressure effect is, how- ever, very small or zero, the changes in solubility µs = µ0s, B B (2) arising from real interactions between solvent and solute. where the upper index 0 denotes a pure phase. For the The model of Kurnik and Reid [8] is possibly one component B in the mixed phase, of the most comprehensive models of solubility of µl = µ∗l( , )+ . solids or liquids in compressed gases. Using volumet- B B T P RT lnaB (3) ric data at constant temperature and composition and µ∗l( , ) some mixing rules, they predict ideal solubility ini- B T P is the chemical potential of the supercooled tially decreasing with pressure, passing through a min- pure liquid B with the dependencies on temperature imum, rising dramatically again as the vapor phase and pressure indicated explicitly. aB is the activity of goes through the critical point and, apparently, going component B in solution and R is the universal gas con- through a maximum at very high pressure and decreas- stant. ing solubility thereafter due to “repulsive forces” be- Replacing (2) and (3) in (1) gives: tween solute and solvent. The steep rise in solubility µ0s = µ∗l + RT a . near the critical point is attributed to real attractive in- B B ln B (4) teractions as evidenced by a vapor-phase fugacity coef- Consider the effect of pressure on activity at T = ficient in the high-pressure gas mixture, which is much constant. Taking derivatives with respect to pressure less than one. The present model, starting from an ideal liquid solution and describing deviations from ideal be- ∂µ0s ∂µ∗l ∂(lna ) B = B + RT B . (5) havior through an energy parameter suggested by the ∂P ∂P ∂P work of Liptay [6] may be considered a simplification T T T of the model of Kurnik and Reid [8]; both models at- For a pure substance tribute enhanced solubility near the critical point to real attractive interactions between solute and solvent. The ∂µ0 ∂µ0 µ0 = B + B , present model cannot predict the minimum in solubil- d B ∂ dP ∂ dT (6) P T T P ity reported by Kurnik and Reid [8] (which may be of commercial importance, for example if a stream of gas where is to be kept as free as possible of impurities; but see ∂µ discussion below) and as mentioned above, neither can = ∂ Vm (7) the maximum reported by them be predicted, as the P T type of forces responsible for the solvatochromic shift and are always attractive. A refined model, which takes into account association of polar solutes for large values of ∂µ = − . the interaction parameter and/or large solute concen- ∂ Sm (8) T P tration, is explained below the discussion. This effect may contribute or eventually account for the mentioned Vm and Sm are the molar volume and the molar entropy, maximum. respectively, of the pure substance. For a process at G. A. Alvarez et al. · Solubility in Supercritical CO2 643 constant temperature the second term on the right in (6) T = 300 K. This leaves ideal solubility practically in- vanishes. Substituting (7) in (5) yields: dependent of pressure up to say 30 MPa. For a real solution a = γ x , where γ is the activ- ∂( ) B B B B 0s = ∗l + lnaB ity coefficient of the solute B in the solution. Replacing Vm Vm RT ∂ (9) P T this in (13) and neglecting the ∆fusionVm term gives or rearranging lnxB = c0 − lnγB. (15) ∂( ) 0s − ∗l ∆ lnaB = Vm Vm = − fusionVm , For the activity coefficient we adopt the Margules ∂ (10) P T RT RT equation where ∆ V is the change in molar volume on melt- w fusion m lnγ = x2 . (16) ing the solid to the supercooled liquid. Presumably, B kT A ∆fusionVm is a positive quantity, so that the slope in (10) is negative and the activity of the solute decreases with xA is the mole fraction of solvent A and k is Boltz- an increase in pressure at constant temperature.
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